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Call an Put Implied Volatilities and the Derivation of Option Implied Trees

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  • V. Moriggia, S. Muzzioli, C. Torricelli

    (University of Modena)

Abstract

Standard methodologies for the derivation of implied trees from option prices are based on the validity of the put-call parity. Muzzioli and Torricelli (2002) propose a methodology which accounts for PCP violations. Based on this latter approach the present paper advances in two main directions. First we propose a different methodology in order to imply the interval of artificial probabilities at each node of the tree. Secondly, we perform an empirical validation of the implied tree obtained, both in the sample and out of sample, by using DAX index options data set covering the period from January 4, 1999 to December 28, 2000. Numerical results are compared with one of the most used standard methodologies, i.e. Derman and Kani’s. The results suggest that the estimation proposed, by taking into account the informational content of both call and put prices, highly improves both the in-the-sample fitting and the out-of-sample performance.
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Suggested Citation

  • V. Moriggia, S. Muzzioli, C. Torricelli, 2007. "Call an Put Implied Volatilities and the Derivation of Option Implied Trees," Frontiers in Finance and Economics, SKEMA Business School, vol. 4(1), pages 35-64, June.
    • Handle: RePEc:ffe:journl:v:4:y:2007:i:1:p:35-64
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    Keywords

    implied binomial tree; smile effect; interval tree;
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • G14 - Financial Economics - - General Financial Markets - - - Information and Market Efficiency; Event Studies; Insider Trading

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